<p>Designing metamaterials for extreme mechanical behavior involves the optimal selection of design parameters. However, identifying these optimal parameters through topology optimization (TO) across a large parametric space requires extensive computational resources. To address this challenge, we propose a novel deep learning framework for metamaterial topology optimization using an enhanced deep super-resolution (EDSR) approach. Generating low-resolution topologies significantly reduces computational cost compared to high-resolution designs. Therefore, an EDSR network is trained to learn the mapping between low- and high-resolution metamaterial topologies. The training dataset is generated using solid isotropic material with penalization (SIMP)-based TO. We demonstrate the proposed approach for the design of mechanical metamaterials targeting objectives such as maximization of bulk modulus, shear modulus, and elastic modulus, and minimization of Poisson’s ratio. Quantitative assessments –including (i) pixel value error, (ii) objective function error, (iii) intersection over union, and (iv) volume fraction error –validate the accuracy of the EDSR-based TO. The proposed framework enables the prediction of high-resolution topologies at <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$192 \times 192$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>192</mn> <mo>×</mo> <mn>192</mn> </mrow> </math></EquationSource> </InlineEquation> pixels from optimized low-resolution topologies at <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$48 \times 48$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>48</mn> <mo>×</mo> <mn>48</mn> </mrow> </math></EquationSource> </InlineEquation> pixels. Once trained, the proposed network predicts these high-resolution topologies with only <InlineEquation ID="IEq3"> <EquationSource Format="TEX">$5-7\%$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>5</mn> <mo>-</mo> <mn>7</mn> <mo>%</mo> </mrow> </math></EquationSource> </InlineEquation> of the computational cost required by conventional SIMP-based TO at the same resolution. Moreover, by adding upscale blocks, the framework can generate smoother, higher-resolution topologies suitable for 3D printing. This approach offers a scalable and efficient solution with strong potential for multidisciplinary metamaterial design applications.</p>

Accelerating metamaterial topology optimization using deep super-resolution networks

期刊论文
发表日期：

2026年2月5日

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Ajendra Singh,
Shubham Saurabh,
Abhinav Gupta,
Rajib Chowdhury

摘要

Designing metamaterials for extreme mechanical behavior involves the optimal selection of design parameters. However, identifying these optimal parameters through topology optimization (TO) across a large parametric space requires extensive computational resources. To address this challenge, we propose a novel deep learning framework for metamaterial topology optimization using an enhanced deep super-resolution (EDSR) approach. Generating low-resolution topologies significantly reduces computational cost compared to high-resolution designs. Therefore, an EDSR network is trained to learn the mapping between low- and high-resolution metamaterial topologies. The training dataset is generated using solid isotropic material with penalization (SIMP)-based TO. We demonstrate the proposed approach for the design of mechanical metamaterials targeting objectives such as maximization of bulk modulus, shear modulus, and elastic modulus, and minimization of Poisson’s ratio. Quantitative assessments –including (i) pixel value error, (ii) objective function error, (iii) intersection over union, and (iv) volume fraction error –validate the accuracy of the EDSR-based TO. The proposed framework enables the prediction of high-resolution topologies at $192 \times 192$ $192 \times 192$ pixels from optimized low-resolution topologies at $48 \times 48$ $48 \times 48$ pixels. Once trained, the proposed network predicts these high-resolution topologies with only $5-7\%$ $5 - 7 %$ of the computational cost required by conventional SIMP-based TO at the same resolution. Moreover, by adding upscale blocks, the framework can generate smoother, higher-resolution topologies suitable for 3D printing. This approach offers a scalable and efficient solution with strong potential for multidisciplinary metamaterial design applications.